Question

rationalize the denominator of \\(\sqrt{\frac{9x}{5y}}\\). assume that all variables represent positive real numbers.\\(\sqrt{\frac{9x}{5y}} = \square\\)

Explanation:

Step1: Split root into fraction of roots

$\sqrt{\frac{9x}{5y}} = \frac{\sqrt{9x}}{\sqrt{5y}}$

Step2: Simplify numerator root

$\sqrt{9x} = 3\sqrt{x}$, so $\frac{3\sqrt{x}}{\sqrt{5y}}$

Step3: Rationalize denominator

Multiply numerator/denominator by $\sqrt{5y}$:
$\frac{3\sqrt{x} \cdot \sqrt{5y}}{\sqrt{5y} \cdot \sqrt{5y}} = \frac{3\sqrt{5xy}}{5y}$

Answer:

$\frac{3\sqrt{5xy}}{5y}$